Problem: Solve for $x$ and $y$ using elimination. ${-2x+6y = 26}$ ${2x-5y = -20}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-2x+6y = 26}\thinspace$ to find $x$ ${-2x + 6}{(6)}{= 26}$ $-2x+36 = 26$ $-2x+36{-36} = 26{-36}$ $-2x = -10$ $\dfrac{-2x}{{-2}} = \dfrac{-10}{{-2}}$ ${x = 5}$ You can also plug ${y = 6}$ into $\thinspace {2x-5y = -20}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(6)}{= -20}$ ${x = 5}$